# Machine Learning for Inductive Theorem Proving

@inproceedings{Jiang2018MachineLF, title={Machine Learning for Inductive Theorem Proving}, author={Yaqing Jiang and P. Papapanagiotou and Jacques D. Fleuriot}, booktitle={AISC}, year={2018} }

Over the past few years, machine learning has been successfully combined with automated theorem provers to prove conjectures from proof assistants. However, such approaches do not usually focus on inductive proofs. In this work, we explore a combination of machine learning, a simple Boyer-Moore model and ATPs as a means of improving the automation of inductive proofs in the proof assistant HOL Light. We evaluate the framework using a number of inductive proof corpora. In each case, our approach…

## 12 Citations

Lemma Synthesis for Automating Induction over Algebraic Data Types

- Computer Science, MathematicsCP
- 2019

An automated prover is presented that searches for a sequence of simplifications and transformations to prove the validity of a given theorem, and in the absence of required lemmas, attempts to synthesize supporting lemma based on terms and expressions witnessed during the search for a proof.

Domain-Specific Language to Encode Induction Heuristics

- Computer ScienceArXiv
- 2019

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, they did not have a systematic way to…

Why Machines Don’t (yet) Reason Like People

- Computer ScienceKI - Künstliche Intelligenz
- 2019

This paper traces their limitations back to two historical developments in AI: the motivation to establish automated theorem-provers for systems of mathematical logic, and the formulation of nonmonotonic systems of reasoning.

A I ] 3 D ec 2 01 9 Self-Learned Formula Synthesis in Set Theory ∗

- Computer Science
- 2019

This work applies machine learning to the task of synthesizing formulas satisfying a collection of semantic properties and instantiation of set variables requiring induction.

Smart Induction for Isabelle/HOL (Tool Paper)

- Computer Science2020 Formal Methods in Computer Aided Design (FMCAD)
- 2020

This work presents smart_induct, an interactive tool that lists promising arguments for the induct tactic without relying on a search that can be used to narrow the search space of automatic inductive provers.

LiFtEr: Language to Encode Induction Heuristics for Isabelle/HOL

- Computer ScienceAPLAS
- 2019

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however they did not have a systematic way to…

SeLFiE: Modular Semantic Reasoning for Induction in Isabelle/HOL

- Computer ScienceArXiv
- 2020

SeLFiE, a domain-specific language to encode experienced users' expertise on how to apply the induct tactic in Isabelle/HOL, facilitates the intricate interaction between syntactic and semantic analyses using semantic constructs while maintaining the modularity of each analysis.

Faster Smarter Induction in Isabelle/HOL with SeLFiE

- Computer ScienceArXiv
- 2020

SeLFiE, a domain-specific language to encode experienced users' expertise on how to apply the induct tactic in Isabelle/HOL is presented, and semantic_induct, an automatic tool to recommend how to applied the induction tactic is presented.

Smart Induction for Isabelle/HOL (System Description)

- Computer ScienceArXiv
- 2020

This work presents smart_induct, a system that lists promising arguments for the induct tactic without relying on a search to solve an inductive problem in any problem domain.

A Blockchain-Based Approach for Collaborative Formalization of Mathematics and Programs

- Computer Science2021 IEEE International Conference on Blockchain (Blockchain)
- 2021

This paper demonstrates a blockchain-based system for collaborative formalization of mathematics and programs incorporating both human labour as well as AI tools, and shows how formalized proofs of different sorting algorithms can be produced collaboratively in this proposed blockchain system.

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